The present invention relates to radio cellular mobile communications and in particular relates to multi-user detection for code division multiple access antenna array receivers.
To cope with the increasing demand for cellular mobile communications it is necessary to find ways to increase system capacity on the reverse link whilst avoiding system complexity.
The cellular mobile communications IS-95 standard describes the use of direct sequence code division multiple access (CDMA) techniques. In such systems, each user is allocated a distinct pseudo-noise (PN) code. The signal from each user is multiplied by a respective code before transmission to the base station. All users transmit using the same radio frequency carrier. The signals from different users will arrive asynchronously due to their different locations and signals from each user may arrive asynchronously due to multipath propagation.
FIG. 1 is an algebraic representation of a CDMA communications link. The vector d contains N consecutive binary data symbols for P users. When these symbols are transmitted, they are subject to multipath distortion. This causes the receiver to observe J versions of each transmitted symbol, which arrive at different times. This effect is defined mathematically by two matrices. Multiplying d by the matrix T repeats each symbol J times. The size NPJ matrix A is diagonal. Its diagonal elements are the positive square roots of the received multipath fading powers for the NP signals received on J paths. This results in the received signal being characterised as the product ATd. The size NPJxc3x97NPJ matrix (R/L)D represents the combined effects of beamforming and of pseudo-noise coding and decoding, where L is the CDMA processing gain. The size NPJxc3x97NPJ matrix R is Hermitian [Horn92, p169] (R. A. Horn and C. R. Johnson, xe2x80x9cMatrix Analysisxe2x80x9d, Cambridge University Press, Cambridge (UK), 1992.) The size NPJxc3x97NPJ matrix D is diagonal [Horn92, p23]. The quantity y=(R/L)DATd+z/L represents the processed received signal plus background noise (the size NPJ vector z/L).
The vector y may be subject to conventional bit detection techniques, e.g. as described in [Proakis95] (J. G. Proakis, xe2x80x9cDigital Communications (3rd Ed)xe2x80x9d, McGraw-Hill, 1995). Alternatively, the capacity of such a system may be improved by employing multi-user detection (MUD) techniques in which information about multiple users is used to detect a desired user. Another way of increasing the capacity of the system is by employing a steerable beam antenna array at the base station. This enables the multiple access interference (MAI) between users transmitting from distinctly different bearings to be reduced. However, the MAI between users transmitting from a similar bearing may not be reduced.
It is known that by using multi-user detection [Moshavi 96] (S. Moshavi, xe2x80x9cMulti-user Detection for DS-CBMA Communicationsxe2x80x9d, IEEE Personal Comms Mag, Vol 34(10), October 1996, pp124-35) or antenna array receivers [Naguib94] (A. F. Naguib, A. Paulraj and T. Kailath, xe2x80x9cCapacity Improvement with Base Station Antenna Arrays in Cellular CDMAxe2x80x9d, IEEE Trans Veh Tech, Vol 43(3), August 1994, pp 691-7), bit error rates considerably lower than those provided by the conventional detector can be achieved for the reverse link of a cellular direct sequence code division multiple access system. Results displayed in FIGS. 8a, b-16a, b confirm these findings for both Additive White Gaussian Noise (AWGN) channels and Rayleigh fading single and multipath channels. Initial beamforming followed by multi-user detection can further decrease bit error rate for these channels (see FIGS. 8b-16b), and hence increase capacity, but at a cost in complexity. FIG. 3 shows a generic receiver employing beamforming followed by multi-user detection. The system is necessarily complicated and computational requirements are high.
Several detection systems exist to provide an estimate of a vector of transmitted bits d, given an output y. The detectors under consideration are the conventional (single user) detector and four multi-user detectors, namely the linear decorrelator detector, the linear minimum mean square error (MMSE) detector, the non-linear decision feedback decorrelator and a form of subtractive interference cancellation (also non-linear). The latter four are usually described for the case of single path transmission (J=1 and T=I, where I is the identity matrix [Horn92, p6]) and in the absence of fading (D=I), that is, when y=(R/L)Ad+z/L.
In the simplest system, single-user detection is employed. The signal from a particular user is detected by correlating the received signal, which is a sum of signals from all transmitting users, with the PN code of the user. The matched filter detector estimates the transmitted bits according to the signs of the real parts of the received output y. The signals from other users interfere with the desired signal and the system capacity is limited by multiple access interference.
The linear decorrelator detector employs an inversion of an estimate of the matrix R/L in order to estimate Ad, where L is the processing gain. A positive definite Hermitian estimate of R, say Rxe2x80x2, is calculated using knowledge of the PN codes, delays, phases and array signatures of the P users. Then Rxe2x80x2/L is inverted using the Cholesky decomposition [Horn92, p407] and the transmitted bits are estimated according to the signs of the real parts of the components of (Rxe2x80x2/L)xe2x88x921y. Estimates of the received signal powers are not required.
The MMSE detector is represented by an NPxc3x97NP matrix C which minimises the following expression:       ∑          k      =      0              NP      -      1        ⁢            ϵ      ⁡              [                              "LeftDoubleBracketingBar"                                          (                                                      C                    ⁢                                          y                      _                                                        -                                      A                    ⁢                                          d                      _                                                                      )                            k                        "RightDoubleBracketingBar"                    2                ]              .  
A closed form expression for C can be determined following a method suggested by [Honig95] (M. Honig, U. Madhow and S. Verdu, xe2x80x9cBlind Adaptive Multiuser Detectionxe2x80x9d, IEEE Trans. Info. Theory, Vol. 41(4), July 1995, pp954-960). The result for C is obtained as:
CMMSE=((R/L)+("sgr"2/Li)Axe2x88x922)xe2x88x921
where "sgr"2 denotes the background noise variance and Axe2x88x921 denotes the matrix inverse operation [Horn92, p14]. The MMSE detector takes into account both the background noise and the received signal powers. In general, the MMSE detector does not enhance the noise as much as the decorrelator and so provides a better bit error rate. Estimates of the received signal powers and the level of background noise are required.
The decision feedback decorrelator makes bit decisions in the order of decreasing received signal powers. Hence these powers need to be estimated. It employs a Cholesky decomposition to factor the positive definite Hermitian matrix R into FHF, where F is a lower triangular matrix and FH is the Hermitian adjoint or transpose [Horn92, p6] of F. The filter {square root over (L)}(FH)xe2x88x921 is applied to the sampled output y to yield:
{square root over (L)}(FH)xe2x88x921y=(F/{square root over (L)})Ad+{square root over (L)}(FH)xe2x88x921z/L
In practice, R can be estimated and hence F. As F/{square root over (L)} is lower triangular, the k-th component of {square root over (L)}(FH)xe2x88x921y does not contain a multiple access interference term for any other bit kxe2x80x2 greater than k. So the 0-th component does not contain an MAI term due to any other bit. A decision for this bit is determined by the sign of the real part of the component. For k greater than 0, we use feedback in the sense that the hard decisions for all bits kxe2x80x3 less than k are used to subtract the MAI from the k-th component of the output. The received signal amplitudes are required for this. Finally, a hard decision for the k-th bit is made.
Subtractive interference cancellation estimates the transmitted bits in order of decreasing received signal powers and hence requires these to be estimated. Initially, the bit estimates provided by a conventional detector are employed. For a given bit, the most recent estimates of all other transmission bits are used to generate an estimate of the MAI from which it suffers. This interference is subtracted from the signal and an updated estimate of the given bit determined by the sign of the real part of the remaining signal.
The present invention seeks to provide a simple to implement base station receiver structure which possesses improved symbol detection characteristics.
In accordance with a first aspect of the invention, there is provided a radio communications system wherein an equivalence relation is defined for a set of users. This equivalence relation is used to group the users into equivalence classes. If CDMA techniques are used, the equivalence relation may be defined according to the temporal information contained in the partial cross-correlations between the PN codes. If an antenna array is incorporated into the receiver structure at the base station, the equivalence relation may be defined according to the spatial signatures of the users. Alternatively, the equivalence relation could be defined using both temporal and spatial information.
If the vectors xi and xj are the spatial signatures corresponding to users i and j, a beamforming term for these 2 users may be defined as (xHi/∥xi∥)(xj/∥xj∥). User classes may be determined so that, if user i and user j are not in equivalent classes, the absolute value of the beamforming term is small in some sense. Such terms can then be replaced by zero, which allows the multiple access interference between users in different equivalence classes to be ignored. This enables a reduction in complexity due to the beamforming.
In the case of dispersive multipath propagation, it may be possible to define more than one spatial signature per user at a particular instant. User equivalence classes may be defined as above if one multipath component (or spatial signature) per user is chosen. For example, the first or the strongest multipath components could be selected. The chosen spatial signature for user i will be denoted xi,0.
Users may be grouped into spatial equivalence classes by choosing a beam pattern threshold "THgr", which lies in the following range: Oxe2x89xa6"THgr"xe2x89xa61. User p and user i are said to be close in bearing if:
xe2x80x83∥(xHp,0/∥xp,0∥)(xi,0/∥xi,0∥)∥2xe2x89xa7"THgr"
A first relation xe2x80x98≈xe2x80x99 between users is defined by:
user p≈user i if ∥(xHp,0/∥xp,0∥)(xi,0/∥xi,0∥)∥2xe2x89xa7"THgr"; and
a second relation xe2x80x98xcx9cxe2x80x99 between users is defined such that:
user pxcx9cuser i if there is a finite sequence of users with indices p0 p1, . . . , pQ, whereby:
user p≈user p0≈user p1≈ . . . ≈user pQ≈user i.
This second relation is an equivalence relation and can be used to determine equivalence classes.
Equivalence classes may be used to reduce the complexity of bit detection when using multi-user detection techniques. These techniques can be applied within the classes, rather than to all users at once.